Facilitating synchronization between a base station and a user equipment

ABSTRACT

Methods and apparatus are provided for facilitating synchronization between a base station (BS) and a user equipment (UE) in a mobile communication system. The UE receives a synchronization signal originated by the BS. The synchronization signal is encoded with a selected cyclically permutable (CP) codeword, the selected CP codeword being selected from a set of CP codewords. Encoding of the synchronization signal is facilitated by a repetitive cyclically permutable (RCP) codeword derivable from the selected CP codeword. The RCP codeword has a plurality of codeword elements each associated with a value, the value of at least one codeword element in the RCP codeword being repeated in another codeword element position in the RCP codeword. And the synchronization signal is decoded in accordance with repetitive structure of the RCP codeword.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.12/342,461, filed on Dec. 23, 2008, which is a continuation ofInternational Patent Application No. PCT/CN2006/002526, filed on Sep.25, 2006. The patent applications identified above are incorporatedherein by reference in their entireties to provide continuity ofdisclosure.

TECHNICAL FIELD

The present application relates to synchronization technology between abase station and a user equipment in a mobile communications system.

BACKGROUND

In a mobile communications system, cell search is a procedure by which auser equipment (UE) acquires time and frequency synchronization in acell and detects a cell ID. The UE is time synchronized when start ofsymbols as well as a radio frame is found. Both symbol timing and frametiming need to be found for completing a cell search.

To improve the symbol timing performance, the synchronization signalsare envisaged to be multiplexed several times in a radio frame. Therebyoutput statistics from a correlator performing symbol timing acquisitioncan be accumulated, and the probability of correct symbol timing isimproved. Furthermore, to allow efficient handover between differentradio systems, it is anticipated that synchronization signals aremultiplexed several times in a radio frame. However, a consequence ofsuch multiplexing is that frame timing may not follow directly fromsymbol timing. Mechanisms are therefore needed that, given symboltiming, frame timing can be determined.

Two classes of synchronization channel (SCH) to be used in cell searchcan be defined: a non-hierarchical SCH and a hierarchical SCH. Anon-hierarchical SCH includes cell-specific signals that serve fortiming acquisition, frequency acquisition, and cell ID detection. Ahierarchical SCH includes at least two signals; a known primarycell-common signal used only for symbol timing acquisition, and acell-specific signal used for frame timing synchronization, frequencysynchronization, and cell ID detection.

Refer to a list of reference documents at the end of this specification,a previously used concept, shown in reference documents [1], [2] and[3], comprises transmission of different signals in SCH slots within aframe. Given symbol timing, signals in the SCH slots are detectedindependently, but together they represent elements of a codeword from asynchronization code. Since SCH is periodically transmitted, thereceiver can detect any cyclic version of a codeword. Thesynchronization code is therefore constructed such that all cyclicshifts of a codeword are unique and no codeword is a cyclic shift ofanother codeword. Thereby frame timing can be uniquely determined from acyclic shift of the detected codeword.

In a fully non-hierarchical SCH, it is foreseen that both cell ID andframe synchronization are detected only from SCH signals within a frame,i.e. no hierarchical cell ID grouping or other channels should beneeded. Correspondingly, in a non-hierarchical solution, a userequipment (UE) would need to decode and compute metrics for 512codewords (cell IDs) and their cyclic shifts at once. Since cell IDdetection is done both initially for finding a home cell andcontinuously for supporting mobility by finding neighbor cells, such anexhaustive procedure may become overly tedious, and consume a lot ofcomputing and power resources in the UE and prolong the cell searchtime. Moreover, as has been discussed for a E-UTRA system, not only cellIDs but also additional cell-specific information may be included in thecell search procedure, e.g. channel bandwidth, number of antennas,cyclic prefix lengths etc. This would require even larger sets ofcodewords that need to be efficiently decoded.

It is desirable to give codewords some form of structure that can beutilized by the receiver.

SUMMARY

It is an object of the present invention to facilitate synchronizationbetween a base station and a user equipment in a mobile communicationsystem.

The foregoing and other objects are achieved by the features of theindependent claims. Further implementation forms are apparent from thedependent claims, the description and the figures.

According to a first aspect, a method is provided for facilitatingsynchronization between a base station (BS) and a user equipment (UE) ina mobile communication system. A set of cyclically permutable (CP)codewords is defined, a plurality of cyclic shifts being derivable fromeach CP codeword, each cyclic shift being distinct from any other cyclicshift derivable from the set of CP codewords. The BS selects a CPcodeword from the set; and encodes the selected CP codeword into asynchronization signal to be sent to the UE, the encoding beingfacilitated by a repetitive cyclically permutable (RCP) codewordderivable from the selected CP codeword, a plurality of cyclic shiftsbeing derivable from the RCP codeword, each cyclic shift derivable fromthe RCP codeword being distinct from any other cyclic shift derivablefrom the RCP codeword. The RCP codeword has a plurality of codewordelements each associated with a value, the value of at least onecodeword element in the RCP codeword being repeated in another codewordelement position in the RCP codeword.

According to a second aspect, a base station is provided. The basestation includes at least one processor configured to:

-   -   define a set of cyclically permutable (CP) codewords, a        plurality of cyclic shifts being derivable from each CP        codeword, each cyclic shift being distinct from any other cyclic        shift derivable from the set of CP codewords;    -   select a CP codeword from the set; and    -   encode the selected CP codeword into a synchronization signal to        be sent to a user equipment (UE), the encoding being facilitated        by a repetitive cyclically permutable (RCP) codeword derivable        from the selected CP codeword, a plurality of cyclic shifts        being derivable from the RCP codeword, each cyclic shift        derivable from the RCP codeword being distinct from any other        cyclic shift derivable from the RCP codeword; the RCP codeword        has a plurality of codeword elements each associated with a        value, the value of at least one codeword element in the RCP        codeword being repeated in another codeword element position in        the RCP codeword.

According to a third aspect, a method is provided for facilitatingsynchronization between a BS and a UE in a mobile communication system.The UE receives a synchronization signal originated by the BS. Thesynchronization signal is encoded with a selected cyclically permutable(CP) codeword, the selected CP codeword being selected from a set of CPcodewords, a plurality of cyclic shifts being derivable from each CPcodeword, each cyclic shift being distinct from any other cyclic shiftderivable from the set of CP codewords, the encoding of thesynchronization signal being facilitated by a repetitive cyclicallypermutable (RCP) codeword derivable from the selected CP codeword, aplurality of cyclic shifts being derivable from the RCP codeword, eachcyclic shift derivable from the RCP codeword being distinct from anyother cyclic shift derivable from the RCP codeword. The RCP codeword hasa plurality of codeword elements each associated with a value, the valueof at least one codeword element in the RCP codeword being repeated inanother codeword element position in the RCP codeword. The UE decodesthe synchronization signal in accordance with repetitive structure ofthe RCP codeword.

According to a fourth aspect, a UE is provided. The UE includes at leastone processor configured to:

-   -   receive a synchronization signal originated by a base station,        the synchronization signal being encoded with a selected        cyclically permutable (CP) codeword, the selected CP codeword        being selected from a set of CP codewords, a plurality of cyclic        shifts being derivable from each CP codeword, each cyclic shift        being distinct from any other cyclic shift derivable from the        set of CP codewords, the encoding of the synchronization signal        being facilitated by a repetitive cyclically permutable (RCP)        codeword derivable from the selected CP codeword, a plurality of        cyclic shifts being derivable from the RCP codeword, each cyclic        shift derivable from the RCP codeword being distinct from any        other cyclic shift derivable from the RCP codeword, the RCP        codeword having a plurality of codeword elements each associated        with a value, the value of at least one codeword element in the        RCP codeword being repeated in another codeword element position        in the RCP codeword; and    -   decode the synchronization signal in accordance with repetitive        structure of the RCP codeword.

According a fifth aspect, a mobile communication system is provided. Thesystem includes a BS operable to communicate with a UE. The BS includesat least one processor configured to:

-   -   define a set of cyclically permutable (CP) codewords, a        plurality of cyclic shifts being derivable from each CP        codeword, each cyclic shift being distinct from any other cyclic        shift derivable from the set of CP codewords;    -   select a CP codeword from the set; and    -   encode the selected CP codeword into a synchronization signal to        be sent to the UE, the encoding being facilitated by a        repetitive cyclically permutable (RCP) codeword derivable from        the selected CP codeword, a plurality of cyclic shifts being        derivable from the RCP codeword, each cyclic shift derivable        from the RCP codeword being distinct from any other cyclic shift        derivable from the RCP codeword, the RCP codeword having a        plurality of codeword elements each associated with a value, the        value of at least one codeword element in the RCP codeword being        repeated in another codeword element position in the RCP        codeword.

The invention thus presents a solution that gives a performance close topure maximum likelihood detection, which is an optimal detection, butwith much lower decoding complexity due to the repetitive structuredesign.

These and other aspects of the invention will be apparent from theembodiments described below.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows performance simulations for an embodiment of the presentinvention and for two methods of prior art;

FIG. 2 shows a mobile communication system (100) including a basestation (120) serving a cell (110) of the system, and a user equipment(130) communicating with the base station in accordance with anembodiment of the present invention.

DETAILED DESCRIPTION

In cell search, the first step is the symbol synchronization. The symboltiming in the non-hierarchical SCH is typically obtained byauto-correlation methods of the received signal, taking certainproperties of the synchronization signal into account. Both symmetricand periodic signals have been suggested in the background art, seereference documents [4] and [5] for symmetric signals and referencedocument [6] for periodic signals. In a hierarchical method, the symboltiming can be obtained by correlation with a replica of the transmittedprimary synchronization channel (P-SCH). Usually there is also some formof frequency synchronization. Once symbol timing and frequencysynchronization is found, frame timing synchronization and cell IDdetection may begin. Symbol- and frequency-synchronization are outsidethe scope of this invention and are assumed to be performed in thesystem.

In WCDMA, the secondary SCH (S-SCH), is transmitted in 15 slots perradio frame. In each such slot, 1 out of 16 S-SCH sequences can be used.These 15 slots are interpreted as the elements of a code word with theS-SCH sequence allocations taken from a Reed-Solomon code. In totalthere are 64 used S-SCH codewords of length 15. These codewords and alltheir cyclic shifts are designed to be unique, i.e. it is a comma-freecode. For decoding a codeword, the receiver computes a soft decodingmetric for all codewords and all their cyclic shifts, i.e. in total64*15 metrics, as is shown in reference document [3]. Thereby, frametiming is directly obtained once the S-SCH is correctly decoded. Thecodewords also correspond to the scrambling code groups. Finally, thecell ID is determined from exhaustive test of all scrambling codes inthe detected scrambling code group, using the common pilot channel(CPICH).

In reference document [7], the comma-free code concept has been adoptedto non-hierarchical SCH. Different periodic signals, which are used bothfor finding symbol timing and cell ID, are transmitted in 5 slots withinthe radio frame. Albeit the signals may be different, they all have thesame time-domain property (periodicity). Hence, different periodicsignals may be multiplexed into the radio frame without loss ofaveraging gain for the symbol timing. The same conclusion also holds ifthe synchronization signals are symmetric. A code is given thatcomprises 236 codewords, requiring 236*5 metric computations fordecoding. As for the hierarchical scheme, the correct decoding of acodeword gives the cell ID and the frame timing. Another code, found byexhaustive search to give 512 codewords of length 4, is used in thenon-hierarchical scheme shown in reference document [8]. The decoding ishere done by the maximum likelihood principle.

Thus the above described background art solutions all rely on themaximum likelihood soft decoding principle, not using any particularstructure of the code as basis for decoding.

The present invention aims to present a synchronization code andassociated method for detecting frame timing synchronization andcell-specific information. The synchronization signal comprises M SCHsequences/symbols being transmitted per radio frame. The allocation ofSCH sequences to the M slots is performed in accordance with the code ofthe present invention, which has a repetitive structure that providesmeans for efficient decoding.

For M SCH symbols per radio frame and N different possible SCHsequences/symbols, a repetitive cyclically permutable code constructionis, according to the invention, proposed to have the followingcharacteristics:

The code should be a cyclically permutable code of length M from analphabet N such that no codeword is a cyclic shift of another and eachcodeword has M distinct cyclic shifts. Codes like this are known from,for instance, reference document [3].

The code should further have a repetitive structure so that at least onecodeword element appears at least two times within the same codeword.This repetitive structure must be followed in each codeword of the code.This is a new feature, proposed by the present invention.

By adding the proposed repetitive structure to the codewords, a decodingmethod can be deduced for which a low number of decoding metrics need tobe computed for detection of the frame synchronization.

The repetitive structure of the codewords gives means for diversitycombining and the associated decoding method utilizes the repetitivestructure in the code to obtain frame synchronization and cell ID. Thedecoding method according to the invention has the followingcharacteristics:

For each of the M SCH slots in the frame, a metric is computed for eachof the N SCH sequences (e.g. obtained from correlation with allcandidate sequences) which relates to the probability that the sequencewas transmitted. This is also done in background art decoding methods.

A set of hypotheses is tested, exploiting the computed metrics and therepetitive structure of the codewords, and one hypothesis that best fitsthe structure of the codeword is selected. This selected hypothesisdetermines which of the M received codeword elements that can bediversity combined. This part of the decoding method, proposed by thepresent invention, is new compared to background art decoding methods.

Diversity combining (summation) of the repeated symbols' metrics isperformed, using information relating to the selected hypothesis. Thisis also a new feature.

Cell ID and final frame synchronization are found from codewords,detected by selecting, for each slot, the sequence with the largestdiversity combined metric. This is also a new feature.

It will later in this specification be shown, for an exemplaryembodiment of the invention, that this decoding method can, compared tomaximum likelihood decoding, reduce the decoding complexity a factorMW/N for even M, and a factor 2W/N for odd M, where M is the codewordlength, N is the number of candidate SCH sequences/symbols and W is thenumber of codewords.

For a given M and N, the decoding complexity and detection performanceof the method according to the invention are, for the method steps ofhypothesis testing, diversity combining and codeword detection,independent of the number of codewords in the code. This is in contrastto a maximum likelihood decoder, for which the decoding complexity growswith the number of codewords and, at the same time, the decodingperformance gets worse.

In the following a more detailed description of the present invention isgiven. It is first showed a couple of exemplary embodiments of how thecode is created by describing how the codewords are generated andthereafter is the decoding procedure described.

Code Construction

The type of code presented in reference document [3] can be used as astarting point when generating a code according to the presentinvention. In reference document [3], a cyclically permutable code oflength M was defined as having the property that no code word is acyclic shift of another, and each codeword has M distinct cyclic shifts.Such a code can uniquely encode frame timing, since all codewords andall cyclic shifts of the codewords are unique, and is thus very suitableto use for synchronization.

Now assume that

$\left( {c_{1},c_{2},\ldots,c_{\lceil\frac{M}{2}\rceil}} \right)$

is a codeword from a cyclically permutable code, such as the code inreference document [3] or any other suitable code, of length

$\left\lceil \frac{M}{2} \right\rceil,{{where}\mspace{14mu} \left\lceil \frac{M}{2} \right\rceil}$

is the smallest integer not less than M/2. Suppose 1≦c_(i)≦N for all i,N is thus the alphabet (the number of possible SCH sequences/symbols)that can be used in each element of the codewords.

A first repetitive cyclically permutable (RCP) code ({tilde over (c)}₁,{tilde over (c)}₂, . . . , {tilde over (c)}_(M)) according to theinvention can then be constructed by:

-   -   for M even:

{tilde over (c)} _(2k-1) ={tilde over (c)} _(2k) =c _(k) , k=1, 2, . . ., M/2,

-   -   and for M odd:

${{\overset{\sim}{c}}_{{2k} - 1} = {{\overset{\sim}{c}}_{2k} = c_{k}}},{k = 1},2,\ldots,{\left\lceil \frac{M}{2} \right\rceil - 1},{{\overset{\sim}{c}}_{M} = {c_{\lceil\frac{M}{2}\rceil}.}}$

We have here created a repetitive cyclically permutable code. To provethat the created repetitive code really is cyclically permutable, andthus fulfils the basic requirement for application to frame timingdetection, we will now show that the codewords ({tilde over (c)}₁,{tilde over (c)}₂, . . . , {tilde over (c)}_(M)) constitute a cyclicallypermutable code in the following proof.

Start of Proof.

First, let M be even and consider a codeword

$\left( {{\overset{\sim}{c}}_{1},{\overset{\sim}{c}}_{2},\ldots,{\overset{\sim}{c}}_{M}} \right) = {\left( {c_{1},c_{1},c_{2},c_{2},\ldots,c_{\frac{M}{2}},c_{\frac{M}{2}}} \right).}$

For the one-step cyclically shifted codeword

$\left( {c_{\frac{M}{2}},c_{1},c_{1},c_{2},\ldots,c_{\frac{M}{2}}} \right)$

to be equal to the non-shifted codeword, we must have

${c_{1} = {c_{2} = {\ldots = c_{\frac{M}{2}}}}},$

which is impossible, since the M/2 symbols long codeword

$\left( {c_{1},c_{2},\ldots,c_{\frac{M}{2}}} \right)$

is cyclically permutable by assumption. Proceeding in the same manner,for every cyclic shift, the same criteria follows

$c_{1} = {c_{2} = {\ldots = {c_{\frac{M}{2}}.}}}$

It is straightforward to see that the same condition appears when M isodd. Hence the codeword ({tilde over (c)}₁, {tilde over (c)}₂, . . . ,{tilde over (c)}_(M)) has M distinct shifts.

Since all the original M/2 symbols long codewords are unique byassumption, and the mapping to the M symbols long codewords isone-to-one, the codewords must also be unique. Therefore, each codewordis unique and has M distinct shifts.

Consider further another codeword

${\left( {{\overset{\sim}{b}}_{1},{\overset{\sim}{b}}_{2},\ldots,{\overset{\sim}{b}}_{M}} \right) = \left( {b_{1},b_{1},b_{2},b_{2},\ldots,b_{\frac{M}{2}},b_{\frac{M}{2}}} \right)},$

for which we showed above that ({tilde over (b)})≠({tilde over (c)}).For the one-step cyclically shifted codeword to be equal to anothercodeword, we must have

${\left( {b_{\frac{M}{2}},b_{1},b_{1},b_{2},\ldots,b_{\frac{M}{2}}} \right) = \left( {c_{1},c_{1},c_{2},c_{2},\ldots,c_{\frac{M}{2}}} \right)},$

which results in that

${b_{1} = {b_{2} = {\ldots = b_{\frac{M}{2}}}}},$

which is impossible. Therefore, any cyclic shift of a codeword is notanother codeword. Hence, the RCP is a cyclically permutable code.

End of Proof.

The first repetitive code created according to this embodiment of theinvention is thus a cyclically permutable code and is therefore suitablefor frame timing synchronization.

A second repetitive cyclically permutable (RCP) code ({tilde over (c)}₁,{tilde over (c)}₂, . . . , {tilde over (c)}_(M)) according to theinvention can for odd M be constructed by:

${\overset{\sim}{c}}_{k} = \left\{ \begin{matrix}c_{k} & {{k = 1},2,\ldots,\left\lceil \frac{M}{2} \right\rceil} \\c_{M + 1 - k} & {{k = {\left\lceil \frac{M}{2} \right\rceil + 1}},\ldots,M}\end{matrix} \right.$

We have here created a second repetitive cyclically permutable code. Wewill now show that the codewords ({tilde over (c)}₁, {tilde over (c)}₂,. . . , {tilde over (c)}_(M)) of this second code constitute acyclically permutable code by the following proof.

Start of Proof.

Consider a codeword

$\left( {{\overset{\sim}{c}}_{1},{\overset{\sim}{c}}_{2},\ldots,{\overset{\sim}{c}}_{M}} \right) = {\left( {c_{1},c_{2},\ldots,c_{\lceil\frac{M}{2}\rceil},c_{{\lceil\frac{M}{2}\rceil} - 1},\ldots,c_{1}} \right).}$

For the one-step cyclically shifted codeword (c₁, c₁, c₂, . . . , c₃,c₂) to the non-shifted codeword, we must have

${c_{1} = {c_{2} = {\ldots = c_{\lceil\frac{M}{2}\rceil}}}},$

which is impossible, since the

$\left\lceil \frac{M}{2} \right\rceil$

symbols long codeword

$\left( {c_{1},c_{2},\ldots,c_{\lceil\frac{M}{2}\rceil}} \right)$

is cyclically permutable by assumption. Proceeding in the same manner,for every cyclic shift, the same criteria follows

$c_{1} = {c_{2} = {\ldots = {c_{\lceil\frac{M}{2}\rceil}.}}}$

Hence the codeword ({tilde over (c)}₁, {tilde over (c)}₂, . . . , {tildeover (c)}_(M)) has M distinct shifts.

Since all the original

$\left\lceil \frac{M}{2} \right\rceil$

symbols long codewords are unique by assumption, and the mapping to theM symbols long codewords is one-to-one, the codewords must also beunique. Therefore, each codeword is unique and has M distinct shifts.

Consider another codeword

${\left( {{\overset{\sim}{b}}_{1},{\overset{\sim}{b}}_{2},\ldots,{\overset{\sim}{b}}_{M}} \right) = \left( {{b_{1}b_{2}},\ldots,b_{\lceil\frac{M}{2}\rceil},b_{{\lceil\frac{M}{2}\rceil} - 1},\ldots,b_{1}} \right)},$

for which we showed above that ({tilde over (b)})≠({tilde over (c)}).For the one-step cyclically shifted codeword to be equal to anothercodeword, we must have

${\left( {b_{1},b_{1},b_{2},\ldots,b_{3},b_{2}} \right) = \left( {c_{1},c_{2},\ldots,c_{\lceil\frac{M}{2}\rceil},c_{{\lceil\frac{M}{2}\rceil} - 1},\ldots,c_{1}} \right)},$

which results in that

${c_{1} = {c_{2} = {\ldots = c_{\lceil\frac{M}{2}\rceil}}}},$

which is impossible. Therefore, any cyclic shift of a codeword is notanother codeword. Hence, it is a cyclically permutable code.

End of Proof.

The second repetitive code created according to the invention is thusalso a cyclically permutable code and is therefore suitable for frametiming synchronization.

The construction of a repetitive cyclically permutable (RCP) codeaccording to the invention assumes a cyclically permutable code to startwith. Such codes can be generated in a number of ways as is clear for askilled person. Hereafter two such exemplary ways are shortly described.

One way of generating cyclically permutable codes in a systematic andsimple fashion could be the following. Suppose that N=64 and M=4. Acyclically permutable code of length 2 can, e.g., be found by the set ofcode words {(c₁, c₂):(1, 2), (1, 3), . . . , (1, 64), (2, 3), (2, 4), .. . , (2, 64), (3, 4), . . . , (3, 64), . . . }. In total there are atmost 63+62+61+ . . . +1=2016 codewords.

A repetitive cyclically permutable (RCP) code according to the inventioncan then be constructed by having these sets of codewords {(c₁, c₂):(1,2), (1, 3), . . . , (1, 64), (2, 3), (2, 4), . . . , (2, 64), (3, 4), .. . , (3, 64), . . . } as a starting point. Following the RCP codeconstruction for even M given above, {tilde over (c)}_(2k-1)={tilde over(c)}_(2k)=c_(k), k=1, 2, . . . , M/2, the new set of extended codewordsaccording to the invention is; {(1, 1, 2, 2), (1, 1, 3, 3), . . . , (1,1, 64, 64), (2, 2, 3, 3), (2, 2, 4, 4), . . . , (2, 2, 64, 64), (3, 3,4, 4), . . . , (3, 3, 64, 64), . . . }.

One other way of generating cyclically permutable codes is described inreference document [3]. A technique (proposed by Bose and Caldwell) forgenerating a cyclically permutable code from a cyclic block code (the RScode) is described in this document. Such techniques may as well be usedas the foundation in the above code construction.

The main principle of the RCP code construction according to theinvention is that it imposes a structure to the codewords. A timerepetitive structure, which will be utilized in the decoder fordetermining time shifts and to provide means for diversity combining ofrepeated symbols, is added to the code.

It should be noted that the concatenation of

$\left( {c_{1},c_{2},\ldots,c_{\lceil\frac{M}{2}\rceil},c_{1},c_{2},\ldots,c_{\lceil\frac{M}{2}\rceil}} \right)$

is a repetition code which would provide larger separation between thesymbols and therefore larger time diversity, but this is not acyclically permutable codeword. Such a code construction is thereforenot suitable for synchronization and does thus not solve our statedproblem.

The code constructions described above uses a repetition factor of 2,i.e. each element is repeated twice within the codeword. Largerrepetition factors could, however, also be considered. Larger repetitionfactors would imply better diversity but would also decrease the numberof codewords. Better diversity in the decoding is favorable, but todecrease the number of codewords is not desirable from a cell searchperspective.

Throughout this description, exemplary embodiments of RCP codesaccording to the invention with repetition factor 2 are mainlydescribed. The invention can however be generalized to more than tworepetitions. This can for instance be done according to the following.

If we have a cyclically permutable code c=(c_(k)) of length n, such thatno codeword is a cyclic shift of another codeword and each codeword hasunique cyclic shifts, the construction of codewords {tilde over(c)}=({tilde over (c)}_(k)) of length n·t can be done by t>1 consecutiverepetitions of each codeword element {tilde over (c)}_(tk−t+1)= . . .={tilde over (c)}_(tk)=c_(k), k=1, 2, . . . , n.

This can also be done, having a cyclically permutable code withcodewords c=(c_(k)) of length n as a starting point, by constructingcodewords {tilde over (c)}=({tilde over (c)}_(k)) of length (n−1)·t+1 byt>1 consecutive repetitions of n−1 codeword elements {tilde over(c)}_(tk−t+1)= . . . ={tilde over (c)}_(tk)=c_(k), k=1, 2, . . . , n−1and {tilde over (c)}_((n−1)·t+1)=c_(n).

There are, as is clear for a person skilled in the art, many ways ofcreating these RCP codes. The methods for creation of repetitivecyclically permutable codes given above are only a couple of exemplaryembodiments of how this can be done. The general idea of the inventioncan be utilized in a number of ways. A skilled person realizes that theinvention can be generalized to imposing any kind of repetitivestructure to a cyclically permutable code.

As long as the repetitive structure is applied for all the codewords inthe code, the decoding procedure according to the invention will reducethe complexity of the decoder. This differs from background artsynchronization codes. In table 4 in reference document [1] it can beseen that for instance groups 15-21 do not contain repetitive codewords.The code defined in the 3GPP standard document does thus not have arepetitive structure for all codewords of the code. The code defined intable 4 in reference document [1] could thus not be used to reduce thedecoding complexity according to the present invention.

Decoding

The decoding procedure will hereafter be described. The decoder shalldetermine the codeword and its cyclic shift. The decoding of the aboveRCP code utilizes the repetitive code structure of the code and is donein four steps that will be described hereafter. These four decodingsteps are:

-   -   calculation of metrics corresponding to probabilities that a        certain value was transmitted for an element in a codeword,    -   hypothesis testing and diversity combining,    -   codeword detection,    -   codeword verification.

Decoding Step 1: Metrics Calculation

For each received synchronization symbol, 1≦m≦M, the receiver computesfor the possible SCH sequences/symbols 1≦k≦N a metric ρ_(km). This may,e.g., be the magnitude of a correlator output, or some other soft outputof a decoder. A large value of ρ_(km) should indicate that sequence kwas transmitted in slot m with high probability. A graph of thiscorrelator output for one slot has thus typically an amplitude peak forthe symbol k that was transmitted and has considerably lower amplitudefor other k.

As a numerical example, if a codeword (1, 1, 2, 2) of length 4 (M=4) hasbeen received, correlations are calculated for each of the four slots inorder to estimate the probabilities for which symbol that wastransmitted in each slot. This is done in order to estimate whichsymbols that were probably transmitted in each slot, in other words,which values the elements of the transmitted codeword probably have. Forthe codeword of this example, codeword (1, 1, 2, 2), the graphs of thecorrelations ρ_(km) for the first and second slots will have a peak forthe value “1” whereas the graphs of the correlations for the third andfourth slots will have a peak for the value “2”.

It may be noted that the correlation values ρ_(km) may in turn beobtained as averages over several radio frames.

Decoding Step 2: Hypothesis Testing and Diversity Combining

The imposed repetitive structure of the code will, in this decodingstep, be exploited in two ways:

-   -   to reduce the number of cyclic shifts to be evaluated,    -   to diversity combine decoder metrics of the elements that have        the same values.

To determine which codeword elements that have the same values, that isto determine which codeword elements that can be diversity combined, thereceiver evaluates a set of hypotheses.

As an example, hypothesis testing is here shown for the RCP code havinga repetition factor 2 given above, created by,

-   -   for M even:

{tilde over (c)} _(2k-1) ={tilde over (c)} _(2k) =c _(k) , k=1, 2, . . ., M/2,

-   -   and for M odd:

${{\overset{\sim}{c}}_{{2k} - 1} = {{\overset{\sim}{c}}_{2k} = c_{k}}},{k = 1},2,\ldots,{\left\lceil \frac{M}{2} \right\rceil - 1},{{\overset{\sim}{c}}_{M} = {c_{\lceil\frac{M}{2}\rceil}.}}$

For even M, there are always only two such hypotheses for thisparticular code, H0 and H1. These hypotheses describe which consecutiveelements of a received codeword {tilde over (r)}=({tilde over (r)}_(i))that, according to each hypothesis, have the same values:

H0: ({tilde over (r)} ₁ ={tilde over (r)} ₂) & ({tilde over (r)} ₃={tilde over (r)} ₄) & . . . & ({tilde over (r)} _(M-1) ={tilde over(r)} _(M))

H1: ({tilde over (r)} ₂ ={tilde over (r)} ₃) & ({tilde over (r)} ₄={tilde over (r)} ₅) & . . . & ({tilde over (r)} _(M) ={tilde over (r)}₁)

Associated with each hypothesis, are M/2 sets, containing the indices tosymbols that can be combined, that is codeword elements that can bediversity combined if the hypothesis is correct.

Having evaluated H0 and H1 and chosen one of them, say H0, as thecorrect one, the metrics of the codeword elements are diversity combinedaccording to the sets of H0. How to generally evaluate hypotheses ismathematically described in more detail later in this section.

For codewords of the length M, where M is odd, a cyclic shift results inthat the M:th codeword element can appear at M positions, thus there areM hypotheses to evaluate.

If there are as many possible cyclic shifts of a codeword as there arehypotheses, the correct hypothesis determines both the elements thatcould be combined and the actual frame timing. Hence no further cyclicshifts would need to be evaluated for detecting the cell ID. Since thehypothesis testing does not include any cell ID detection, it would inthis case mean that, frame timing can be obtained before and withouthaving to determine the cell ID. It can be observed that in the specialcase of M being odd and all codewords have the property {tilde over(c)}_(M)≠{tilde over (c)}₁ & {tilde over (c)}_(M)≠{tilde over(c)}_(M-1), there are as many possible cyclic shifts of the codewords asthere are hypotheses, see the following example.

If we, for example, analyze a codeword (1, 1, 2, 2, 3) and its cyclicshifts (3, 1, 1, 2, 2), (2, 3, 1, 1, 2), (2, 2, 3, 1, 1) and (1, 2, 2,3, 1), we realize that each of these shifts corresponds to onehypothesis each, i.e., in total 5 hypotheses.

H0: ({tilde over (r)} ₁ ={tilde over (r)} ₂) & ({tilde over (r)} ₃={tilde over (r)} ₄)

H1: ({tilde over (r)} ₂ ={tilde over (r)} ₃) & ({tilde over (r)} ₄={tilde over (r)} ₅)

H2: ({tilde over (r)} ₁ ={tilde over (r)} ₅) & ({tilde over (r)} ₃={tilde over (r)} ₄)

H3: ({tilde over (r)} ₁ ={tilde over (r)} ₂) & ({tilde over (r)} ₄={tilde over (r)} ₅)

H4: ({tilde over (r)} ₁ ={tilde over (r)} ₅) & ({tilde over (r)} ₂={tilde over (r)} ₃)

Clearly, since all of the 5 cyclic shifts belong to differenthypotheses, the correct hypothesis determines which elements to combineand, additionally, also the actual frame timing.

If we instead analyze a codeword (1, 1, 2, 2, 2) and its cyclic shifts(2, 1, 1, 2, 2), (2, 2, 1, 1, 2), (2, 2, 2, 1, 1) and (1, 2, 2, 2, 1),by testing the hypotheses H0-H4 defined above, we will be able todetermine which two elements to diversity combine with each other. But,the frame timing may not be obtained directly from the correcthypothesis because more than one codeword are true under eachhypothesis. E.g., both (1, 1, 2, 2, 2) and (2, 2, 1, 1, 2) are trueunder H0, both (2, 1, 1, 2, 2) and (2, 2, 2, 1, 1) are true under H1etc.

The hypothesis testing and diversity combining procedures will now bedescribed mathematically.

According to the invention, hypotheses should be evaluated and diversitycombining should be performed by calculating, for each hypothesis h andits associated index sets R_(hj), for all j:

$\begin{matrix}{{{D_{kj}(h)} = {\underset{m \in R_{hj}}{\Sigma}\rho_{km}}},} & (1)\end{matrix}$

and choose the hypothesis Hx, for which

$\begin{matrix}{{x = {\arg \mspace{14mu} {\max\limits_{h}\mspace{14mu} {\underset{j}{\Sigma}\mspace{14mu} {\max\limits_{k}\mspace{14mu} {D_{kj}(h)}}}}}},} & (2)\end{matrix}$

where ρ_(km) relates to the probability that sequence k was transmittedin slot m and R_(hj) are index sets indicating sets of codeword elementsunder hypothesis h having the same value.

In equation 1, the diversity combining of the metrics is done accordingto the timing which the hypothesis defines, that is diversity combiningis here performed in accordance with the hypothesis.

By the hypothesis testing and diversity combining in decoding step 2according to the invention, the decoder has both narrowed down thepossible cyclic shifts and computed new metrics D_(kj) by diversitycombining. Less complex computation in the following decoding steps,compared to background art methods, can therefore be achieved.

In an illustrative numerical example for a code with M=4, the codeword(1, 1, 2, 2) and its cyclic shifts (2, 1, 1, 2), (2, 2, 1, 1) and (1, 2,2, 1) can be considered. For determining which codeword elementcorrelations to diversity combine, out of the in total 4 codewordelements, two hypotheses are tested:

H0: ({tilde over (r)} ₁ ={tilde over (r)} ₂) & ({tilde over (r)} ₃={tilde over (r)} ₄)

H1: ({tilde over (r)} ₁ ={tilde over (r)} ₄) & ({tilde over (r)} ₂={tilde over (r)} ₃)

The codewords (1, 1, 2, 2) and (2, 2, 1, 1) are captured under H0, andthe other two under H1. Index sets associated with hypothesis H0 can bedefined as R₀₁={1, 2} and R₀₂={3, 4}. These index sets here correspondto the codeword elements that, according to hypothesis H0, have the samevalues and therefore also should be diversity combined. The first andthe second codeword element have the same values in H0 and the third andthe fourth codeword elements also have the same value, index setsR₀₁={1, 2} and R₀₂={3, 4} can therefore be derived. For hypothesis H1,index sets R₁₁={1, 4} and R₁₂={2, 3} can be defined in the same way. Atthis step of hypothesis testing it is not necessary to decode anycodeword, only a correct hypothesis is sought. Once the hypothesis isdetected (H0 or H1), the correlations are diversity combined accordingto the detected hypothesis, and decoding of cell ID starts. Note thatthe frame timing is not directly obtained once the correct hypothesis isdetermined, there are still a number of codewords that belong to thesame hypothesis, e.g. (1, 1, 2, 2) and (2, 2, 1, 1) for H0, and frametiming is obtained first when one of theses codewords belonging to thenhypothesis is chosen as the transmitted codeword.

As previously the in the numerical example in decoding step 1 (metricscalculation) above, the graphs of the correlations ρ_(km) for thecodeword (1, 1, 2, 2) will have a peak for the value “1” in the firstand second slots whereas the graphs of the correlations ρ_(km) for thethird and fourth slots will have a peak for the value “2”.

If these peaks all have amplitude=1, then a perfect reception of thecodeword (1, 1, 2, 2) would result in ρ₁₁=ρ₁₂=ρ₂₃=ρ₂₄=1 (amplitude) andall other √_(km)=0 (amplitude). Equation 1 above then adds thesecorrelation vectors together according to the index sets correspondingto the two hypotheses, that is for H0 index sets R₀₁={1, 2} and R₀₂={3,4} are used and for hypothesis H1 index sets R₁₁={1, 4} and R₁₂={2, 3}are used.

For H0, the correlations for the index set R₀₁={1, 2} are first summedfor the received codeword (1, 1, 2, 2). Both first and second elementsof the codeword have the value “1”. ρ_(km) for both the first and thesecond element thus have a peak for value “1” and these the correlationsρ_(km) are summed together to a big peak for the value “1”. This peakhas an amplitude=2, since ρ₁₁=ρ₁₂=1. The graph of Dkj(0) in equation 1will thus be a correlation graph having a peak of amplitude=2 for thevalue “1” and amplitude zero for the rest of the values. Then thecorrelations for the index set R₀₂={3, 4} are also summed for thereceived codeword (1, 1, 2, 2). Since both third and fourth elements ofthe codeword have the value “2” the correlations are added together to abig peak for the value “2”, this peak having an amplitude=2. The graphof Dkj(0) in equation 1 will thus be a correlation graph having a peakof amplitude 2 for the value “2” and amplitude zero for the rest of thevalues.

For hypothesis H0, equation 2 then searches for the maximum values ofDkj(0) corresponding to R01 and R02 and adds these maximum valuestogether. This results in

${{\underset{j}{\Sigma}\mspace{14mu} {\max\limits_{k}\mspace{14mu} {D_{kj}(0)}}} = 4},$

since both Dkj(0) corresponding to R01 and Dkj(0) corresponding to R02have a peak amplitude=2.

If the same procedure is performed for hypothesis H1 for the codeword(1, 1, 2, 2), the summations of correlations ρ_(km) according tohypothesis H1 using index sets R₁₁={1, 4} and R₁₂={2, 3} in equation 1will result in Dkj(1):s having two peaks of amplitude 1. This since, forexample, addition according to index set R₁₁={1, 4} adds the first andthe fourth codeword element. The correlation curves ρ_(km) for the firstand fourth element have peaks in different positions since the elementshave different values, the curve for the first element has a peak forthe position of value “1” and the curve for the fourth element has apeak for the position of value “2”. When these correlations are addedtogether the graph of the summation thus has two peaks of amplitude 1,one for value “1” and one for value “2”.

For hypothesis H1, equation 2 then searches for the maximum values ofDkj(1) corresponding to R11 and R12 and adds these maximum valuestogether. This results in

${{\underset{j}{\Sigma}\mspace{14mu} {D_{kj}(1)}} = 2},$

since both Dkj(1) corresponding to R11 and Dkj(1) corresponding R12 havea maximum amplitude=1.

Thus, using the hypotheses H0 and H1 defined above in this example, itfollows that

${\underset{j}{\Sigma}\mspace{14mu} {\max\limits_{k}\mspace{14mu} {D_{kj}(0)}}} = 4$

for H0 and

${\underset{j}{\Sigma}{D_{kj}(1)}} = 2$

for H1. This shows that, the energy of all the symbols are added underhypothesis H0, whereas under the wrong hypothesis (H1) only the energyof one symbol per index set is captured. We therefore get a larger valuefor hypothesis H0 here, since H0 is the correct hypothesis. This can beused for selecting hypothesis, simply by choosing the hypothesisrendering the largest value of D_(kj).

Decoding Step 3: Codeword Detection

In the codeword detection step, the codeword elements can be determinedin at least two different ways. One way of detecting the elements is newfor the present invention and one way is derived from maximum likelihoodcriterion.

First the new detection method is presented. According to this detectionmethod the detection is performed as:

-   -   for the chosen hypothesis Hx, for all j, and pεR_(xj), let the        detected codeword s=(s_(p)) be:

$\begin{matrix}{s_{p} = {\arg \mspace{14mu} {\max\limits_{k}\mspace{14mu} {{D_{kj}(x)}.}}}} & (3)\end{matrix}$

This procedure allocates the codeword elements from the diversitycombined metrics D_(kj)(x).

The computed metrics D_(kj) from equation 1 are reused in equation 3 forcodeword decoding, which is performed by a single maximizationoperation. If the hypothesis test in decoding step 2 is accurate,metrics have already been correctly combined in decoding step 2 and themaximization step in equation 3 should assure good performance.

Since the number of tested hypotheses in general is much lower than thenumber of codewords and their cyclic shifts, less metric computationsare foreseen and a lower decoding complexity can be maintained. Incomparison, the maximum likelihood scheme in reference document [3],computes one metric

$\sum\limits_{i = 1}^{M}\; \rho_{{\overset{\sim}{c}}_{i}i}$

for each codeword ({tilde over (c)}₁, {tilde over (c)}₂, . . . , {tildeover (c)}_(M)) and each cyclic shift thereof and then compares all ofthem to get the maximum one.

It is noted that in the above method described in decoding steps 1-3,after the choice of hypothesis, the number of remaining and eligiblecyclic shifts of the codewords has been reduced, only those under thechosen Hx remain. For the exemplary code described on page 11, for evenM, the number of time shifts has been reduced by 2 and for odd M it isreduced by a factor M.

As was mentioned above, a method derived from a maximum likelihoodcriterion can also be used for codeword detection in decoding step 3.Codeword detection according to this method is, for the chosenhypothesis Hx and all codewords {tilde over (c)}εΦ, where the set Φcontains the codewords and cyclic shifts thereof that may be true underHx, performed as:

$\begin{matrix}{{s = {\arg \mspace{14mu} {\max\limits_{\overset{\sim}{c} \in \Phi}{\sum\limits_{i = 1}^{M}\; \rho_{{\overset{\sim}{c}}_{i}i}}}}},} & (4)\end{matrix}$

where s is the detected codeword.

It should be noted that, if this maximum likelihood criterion is usedfor the present invention it still differs from pure maximum likelihoodmethods as the one shown in reference document [3]. According to thisinvention decoding steps 1 and 2 are first performed according to theinvention and the maximum likelihood criterion is only used in decodingstep 3. That is, only time shifts under the chosen hypothesis areevaluated in the method. In pure maximum likelihood methods as the onedescribed in reference document [3], all codewords and all cyclic shiftsthereof are evaluated, not only the ones under the chosed hypothesis asin the present invention.

Decoding Step 4: Codeword Verification

Finally it is verified whether the resulting codeword (s₁, s₂, . . . ,s_(M)) is a valid cyclically shifted codeword. This is done by comparingit to all possible codewords and cyclic shifts of codewords under thechosen hypothesis. If the detected codeword is a valid codeword, theframe timing and cell ID is determined correctly. If it is not, adecoding error should be declared.

Note that the calculations also in this step are reduced by the presentinvention since the detected codeword only has to be compared topossible codewords and cyclic shifts of codewords under the chosenhypothesis and not to all possible codewords and cyclic shifts ofcodewords.

Performance Evaluation

The whole decoding procedure has now been presented. In the followingsections the performance and the complexity of the present invention isdescribed.

The main goal of the present invention is to lower the decodingcomplexity. The performance of the invention in terms of decodingcomplexity is hereafter discussed. Decoding complexity is analysed interms of number of operations per decoded codeword, assuming arepetition factor of 2, for the exemplary code given on page 11.

For the RCP code according to the invention in decoding step 1 and 2,there will be N·M/2·H [elements/index set*index sets*hypotheses]additions of correlation values where H is the number of hypotheses (H=2for M even, and H=M for M odd). So the number of computations is linearor quadratic in the code length M, linear in the sequence space N but,importantly, for a given N and M, independent of the number of codewordsof the code. In decoding step 3, the maximum operator is applied M/2times on a vector of length N.

As a comparison, for completing a pure maximum likelihood decoding,according to for example reference document [3], all codewords andcyclic shifts are evaluated according to

$\sum\limits_{i = 1}^{M}\; {\rho_{{\overset{\sim}{c}}_{i}i}.}$

If the code has W codewords, there will in total be W·M²[codewords*elements/codeword*cyclic shifts] additions of correlationvalues, where the square on M accounts for the cyclic shifts. So thenumber of computations is always quadratic in the code length M, linearin the number of codewords but independent of the sequence space N. Thefinal maximum operator is applied 1 time to a vector of length W·M.

Thus, the proposed RCP code according to the invention will reduce thedecoding complexity in the correlation computations and maximizationoperations for codes with large amount of codewords (W>>N) and/or longcode lengths. For even M, the decoding complexity reduction is a factorMW/N and for odd M, a factor 2W/N. Thus the RCP code is suitable to,e.g., non-hierarchical cell search, where a larger number of codewordsmust be handled.

In FIG. 1, the code described above in the section of code construction,having the set of codewords: {(1, 1, 2, 2), (1, 1, 3, 3), . . . , (1, 1,64, 64), (2, 2, 3, 3), (2, 2, 4, 4), . . . , (2, 2, 64, 64), (3, 3, 4,4), . . . , (3, 3, 64, 64), . . . }, has been numerically evaluated.

From the code, 1024 codewords have been selected. Simulations are donein an OFDM simulator, following the working assumptions of E-UTRA. Thesynchronization sequences and the detector are described further inreference document [9]. The error probabilities of three decodingmethods are plotted;

-   -   1) Maximum likelihood (ML) detection (optimal).    -   2) The proposed method of the present invention.    -   3) A method which decodes each codeword element independently,

${s_{m} = {\arg \mspace{14mu} {\max\limits_{k}\mspace{14mu} \rho_{km}}}},$

not using any diversity combining.

Method 3 can be regarded as a method not offering any coding gain, asthe elements are decoded individually. For methods 2 and 3, an errorevent is counted also if a decoding error is declared.

It can be seen that the proposed method 2 is close to the optimal MLmethod within a fraction of one dB. The loss of not using the inherentdiversity structure in the code is shown by the much worse performanceof the last method, method 3. Hence the suggested method 2 is expectedto not significantly increase the cell search time, while having a muchsimpler decoding procedure than ML.

In the ML decoding according to method 1, the correct codeword is foundif its metric is larger than those of all the other codewords. Hence,increasing the number of codewords, the error probability will becomeworse, as more erroneous codeword candidates need to be compared. Thesame effect occurs for ML decoding if M increases, as there are thenmore cyclic shifts to consider.

Therefore, the performance gain of ML over the proposed decodingalgorithm of the present invention will decrease as the number ofcodewords becomes larger. Thus the RCP code is suitable to e.g. anon-hierarchical cell search, where a larger number of codewords must becoped with.

The invention can further be used in all applications where thesynchronization signals, transmitted to support and alleviate the timingacquisition in the receiver, also carry some information, such as anidentification number of a transmitter etc. One such application is thecell search procedure in the cellular systems. A skilled person realizesthat there are more such applications for the invention.

The given synchronization code of the invention, can be used in bothnon-hierarchical and hierarchical synchronization channels. Theinvention is also not restricted to OFDM signals, it can be used for allkinds of telecommunication systems as is clear to a skilled person.

The repetitive code structure may also be utilized in the channelestimation and can further be used in other signaling in atelecommunication system.

The code creation and decoding according to the invention may bemodified by those skilled in the art, as compared to the exemplaryembodiments described above.

REFERENCE DOCUMENTS

-   [1] 3GPP TS 25.213 v7.0.0, “Spreading and modulation (FDD)”.-   [2] Y.-P. E. Wang and T. Ottosson, “Cell Search in W-CDMA”, IEEE J.    Sel. Areas Commun., vol. 18, pp. 1470-1482, August 2000.-   [3] S. Sriram and S. Hosur, “Cyclically Permutable Codes for Rapid    Acquisition in DS-CDMA Systems with Asynchronous Base Stations”,    IEEE J. Sel. Areas Commun., vol. 19, pp. 83-94, January 2000.-   [4] M. Tanda, “Blind Symbol-Timing and Frequency-Offset Estimation    in OFDM Systems with Real Data Symbols,” IEEE Trans. Commun., vol.    52, pp. 1609-1612, October 2004.-   [5] B. M. Popovic, “Synchronization signals for timing acquisition    and information transmission”, PCT/CN2006/000076, Huawei, 2006.-   [6] T. M. Schmidl and D. C. Cox, “Robust Frequency and Timing    Synchronization for OFDM”, IEEE Trans. Commun., vol. 45, pp.    1613-1621, December 1997.-   [7] ETRI, “Cell Search Scheme for EUTRA”, R1-060823, Athens, Greece,    Mar. 27-31, 2006.-   [8] Huawei, “Additional Link-level Evaluation of Cell Search Times    for Non-hierarchical and Hierarchical SCH Signals”, R1-061817,    Cannes, France, Jun. 27-30, 2006.-   [9] Huawei, “Cell Search Times of Hierarchical and Non-hierarchical    SCH Signals”, R1-061248, Shanghai, China, May 8-12, 2006.-   [10] Huawei, “System-level Evaluation of Cell Search Times for    Non-hierarchical and Hierarchical SCH Signals”, R1-061818, Cannes,    France, Jun. 27-30, 2006.

What is claimed is:
 1. A method of facilitating synchronization betweena base station (BS) and a user equipment (UE) in a mobile communicationsystem, comprising: defining a set of cyclically permutable (CP)codewords, a plurality of cyclic shifts being derivable from each CPcodeword, each cyclic shift being distinct from any other cyclic shiftderivable from the set of CP codewords; selecting, by the BS, a CPcodeword from the set; and encoding, by the BS, the selected CP codewordinto a synchronization signal to be sent to the UE, the encoding beingfacilitated by a repetitive cyclically permutable (RCP) codewordderivable from the selected CP codeword, a plurality of cyclic shiftsbeing derivable from the RCP codeword, each cyclic shift derivable fromthe RCP codeword being distinct from any other cyclic shift derivablefrom the RCP codeword, wherein the RCP codeword has a plurality ofcodeword elements each associated with a value, the value of at leastone codeword element in the RCP codeword being repeated in anothercodeword element position in the RCP codeword.
 2. The method of claim 1,wherein the set of CP codewords is expressed as:$\left( {c_{1},c_{2},{\ldots \; c_{i}\ldots},c_{\lceil\frac{M}{2}\rceil}} \right),{{where}\mspace{14mu} \left\lceil \frac{M}{2} \right\rceil}$is the smallest integer not less than M/2, 0≦c_(i)≦N, 1≦i≦M for all i,M, N are positive integers.
 3. The method of claim 2, wherein N=64, M=4,and the set of CP codewords is: {(c₁, c₂):(1, 2), (1, 3), . . . , (1,64), (2, 3), (2, 4), . . . , (2, 64), (3, 4), . . . , (3, 64), . . .(63, 64)}, and in total there are at most 63+62+61+ . . . +1=2016 CPcodewords.
 4. The method of claim 2, wherein the RCP codeword isexpressed as ({tilde over (c)}₁, {tilde over (c)}₂, . . . , {tilde over(c)}_(M)) with {tilde over (c)}_(2k-1)={tilde over (c)}_(2k)=c_(k), k=1,2, . . . , M/2, where M is an even number.
 5. The method of claim 2,wherein the RCP codeword is expressed as ({tilde over (c)}₁, {tilde over(c)}₂, . . . , {tilde over (c)}_(M)) with${{\overset{\sim}{c}}_{{2k} - 1} = {{\overset{\sim}{c}}_{2k} = c_{k}}},{k = 1},2,\ldots,{\left\lceil \frac{M}{2} \right\rceil - 1},{{\overset{\sim}{c}}_{M} = {c_{\lceil\frac{M}{2}\rceil}.}}$where M is an odd number.
 6. The method of claim 4, wherein N=64, M=4,and the RCP codeword is included in the following: {(1, 1, 2, 2), (1, 1,3, 3), . . . , (1, 1, 64, 64), (2, 2, 3, 3), (2, 2, 4, 4), . . . , (2,2, 64, 64), (3, 3, 4, 4), . . . , (3, 3, 64, 64), . . . (63, 63, 64,64)}.
 7. The method of claim 2, wherein M=4, and the set of CP codewordsis expressed as (c₁, c₂), the plurality of cyclic shifts being derivablefrom each CP codeword is expressed as: (c₁, c₂) and (c₂, c₁).
 8. Themethod of claim 4, wherein M=4, the RCP codeword is expressed as ({tildeover (c)}₁, {tilde over (c)}₂, . . . , {tilde over (c)}_(M))=(c₁, c₁,c₂, c₂), and the plurality of cyclic shifts being derivable from the RCPcodeword is expressed as: (c₂, c₁, c₁, c₂), (c₂, c₂, c₁, c₁), (c₁, c₂,c₂, c₁) and (c₁, c₁, c₂, c₂).
 9. A base station, comprising at least oneprocessor configured to: define a set of cyclically permutable (CP)codewords, a plurality of cyclic shifts being derivable from each CPcodeword, each cyclic shift being distinct from any other cyclic shiftderivable from the set of CP codewords; select a CP codeword from theset; and encode the selected CP codeword into a synchronization signalto be sent to a user equipment (UE), the encoding being facilitated by arepetitive cyclically permutable (RCP) codeword derivable from theselected CP codeword, a plurality of cyclic shifts being derivable fromthe RCP codeword, each cyclic shift derivable from the RCP codewordbeing distinct from any other cyclic shift derivable from the RCPcodeword, wherein the RCP codeword has a plurality of codeword elementseach associated with a value, the value of at least one codeword elementin the RCP codeword being repeated in another codeword element positionin the RCP codeword.
 10. The base station of claim 9, wherein the set ofCP codewords is expressed as:$\left( {c_{1},c_{2},{\ldots \; c_{i}\ldots},c_{\lceil\frac{M}{2}\rceil}} \right),{{where}\mspace{14mu} \left\lceil \frac{M}{2} \right\rceil}$is the smallest integer not less than M/2, 0≦c_(i)≦N, 1≦i≦M, for all i,M, N are positive integers.
 11. The base station of claim 10, whereinthe RCP codeword is expressed as ({tilde over (c)}₁, {tilde over (c)}₂,. . . , {tilde over (c)}_(M)) with {tilde over (c)}_(2k-1)={tilde over(c)}_(2k)=c_(k), k=1, 2, . . . , M/2, where M is an even number.
 12. Thebase station of claim 10, wherein the RCP codeword is expressed as({tilde over (c)}₁, {tilde over (c)}₂, . . . , {tilde over (c)}_(M))with${{\overset{\sim}{c}}_{{2k} - 1} = {{\overset{\sim}{c}}_{2k} = c_{k}}},{k = 1},2,\ldots,{\left\lceil \frac{M}{2} \right\rceil - 1},{{\overset{\sim}{c}}_{M} = {c_{\lceil\frac{M}{2}\rceil}.}}$where M is an odd number.
 13. The base station of claim 10, wherein M=4,and the set of CP codewords is expressed as (c₁, c₂), the plurality ofcyclic shifts being derivable from each CP codeword is expressed as:(c₁, c₂) and (c₂, c₁).
 14. The base station of claim 11, wherein M=4,the RCP codeword is expressed as ({tilde over (c)}₁, {tilde over (c)}₂,. . . , {tilde over (c)}_(M))=(c₁, c₁, c₂, c₂), and the plurality ofcyclic shifts being derivable from the RCP codeword is expressed as:(c₂, c₁, c₁, c₂), (c₂, c₂, c₁, c₁), (c₁, c₂, c₂, c₁) and (c₁, c₁, c₂,c₂).
 15. A method of facilitating synchronization between a base station(BS) and a user equipment (UE) in a mobile communication system,comprising: receiving, by the UE, a synchronization signal originated bythe BS, wherein the synchronization signal is encoded with a selectedcyclically permutable (CP) codeword, the selected CP codeword beingselected from a set of CP codewords, a plurality of cyclic shifts beingderivable from each CP codeword, each cyclic shift being distinct fromany other cyclic shift derivable from the set of CP codewords, theencoding of the synchronization signal being facilitated by a repetitivecyclically permutable (RCP) codeword derivable from the selected CPcodeword, a plurality of cyclic shifts being derivable from the RCPcodeword, each cyclic shift derivable from the RCP codeword beingdistinct from any other cyclic shift derivable from the RCP codeword,the RCP codeword having a plurality of codeword elements each associatedwith a value, the value of at least one codeword element in the RCPcodeword being repeated in another codeword element position in the RCPcodeword; and decoding the synchronization signal in accordance withrepetitive structure of the RCP codeword.
 16. The method of claim 15,wherein the set of CP codewords is expressed as:$\left( {c_{1},c_{2},{\ldots \; c_{i}\ldots},c_{\lceil\frac{M}{2}\rceil}} \right),{{where}\mspace{14mu} \left\lceil \frac{M}{2} \right\rceil}$is the smallest integer not less than M/2, 0≦c_(i)≦N, 1≦i≦M for all i,M, N are positive integers.
 17. The method of claim 16, wherein the RCPcodeword is expressed as ({tilde over (c)}₁, {tilde over (c)}₂, . . . ,{tilde over (c)}_(M)) with {tilde over (c)}_(2k-1)={tilde over(c)}_(k)=c_(k), k=1, 2, . . . , M/2, where M is an even number.
 18. Themethod of claim 16, wherein the RCP codeword is expressed as ({tildeover (c)}₁, {tilde over (c)}₂, . . . , {tilde over (c)}_(M)) with${{\overset{\sim}{c}}_{{2k} - 1} = {{\overset{\sim}{c}}_{2k} = c_{k}}},{k = 1},2,\ldots,{\left\lceil \frac{M}{2} \right\rceil - 1},{{\overset{\sim}{c}}_{M} = {c_{\lceil\frac{M}{2}\rceil}.}}$where M is an odd number.
 19. The method of claim 16, wherein M=4, andthe set of CP codewords is expressed as (c₁, c₂), the plurality ofcyclic shifts being derivable from each CP codeword is expressed as:(c₁, c₂) and (c₂, c₁).
 20. The method of claim 17, wherein M=4, the RCPcodeword is expressed as ({tilde over (c)}₁, {tilde over (c)}₂, . . . ,{tilde over (c)}_(M))=(c₁, c₁, c₂, c₂), and the plurality of cyclicshifts being derivable from the RCP codeword is expressed as: (c₂, c₁,c₁, c₂), (c₂, c₂, c₁, c₁), (c₁, c₂, c₂,c₁) and (c₁, c₂, c₂, c₂).
 21. Auser equipment, comprising at least one processor configured to: receivea synchronization signal originated by a base station, wherein thesynchronization signal is encoded with a selected cyclically permutable(CP) codeword, the selected CP codeword being selected from a set of CPcodewords, a plurality of cyclic shifts being derivable from each CPcodeword, each cyclic shift being distinct from any other cyclic shiftderivable from the set of CP codewords, the encoding of thesynchronization signal being facilitated by a repetitive cyclicallypermutable (RCP) codeword derivable from the selected CP codeword, aplurality of cyclic shifts being derivable from the RCP codeword, eachcyclic shift derivable from the RCP codeword being distinct from anyother cyclic shift derivable from the RCP codeword, the RCP codewordhaving a plurality of codeword elements each associated with a value,the value of at least one codeword element in the RCP codeword beingrepeated in another codeword element position in the RCP codeword; anddecode the synchronization signal in accordance with repetitivestructure of the RCP codeword.
 22. The user equipment of claim 21,wherein the set of CP codewords is expressed as:$\left( {c_{1},c_{2},{\ldots \; c_{i}\ldots},c_{\lceil\frac{M}{2}\rceil}} \right),{{where}\mspace{14mu} \left\lceil \frac{M}{2} \right\rceil}$is the smallest integer not less than M/2, 0≦c_(i)≦N, 1≦i≦M for all i,M, N are positive integers.
 23. The user equipment of claim 22, whereinthe RCP codeword is expressed as ({tilde over (c)}₁, {tilde over (c)}₂,. . . , {tilde over (c)}_(M)) with {tilde over (c)}_(2k-1)={tilde over(c)}_(2k)=c_(k), k=1, 2, . . . , M/2, where M is an even number.
 24. Theuser equipment of claim 22, wherein the RCP codeword is expressed as({tilde over (c)}₁, {tilde over (c)}₂, . . . , {tilde over (c)}_(M))with${{\overset{\sim}{c}}_{{2k} - 1} = {{\overset{\sim}{c}}_{2k} = c_{k}}},{k = 1},2,\ldots,{\left\lceil \frac{M}{2} \right\rceil - 1},{{\overset{\sim}{c}}_{M} = {c_{\lceil\frac{M}{2}\rceil}.}}$where M is an odd number.
 25. The user equipment of claim 22, whereinM=4, and the set of CP codewords is expressed as (c₁, c₂), the pluralityof cyclic shifts being derivable from each CP codeword is expressed as:(c₁, c₂) and (c₂, c₁).
 26. The user equipment of claim 23, wherein M=4,the RCP codeword is expressed as ({tilde over (c)}₁, {tilde over (c)}₂,. . . , {tilde over (c)}_(M))=(c₁, c₁, c₂, c₂), and the plurality ofcyclic shifts being derivable from the RCP codeword is expressed as:(c₂, c₁, c₁, c₂), (c₂, c₂, c₁, c₁), (c₁, c₂, c₂, c₁) and (c₁, c₁, c₂,c₂).
 27. A mobile communication system, comprising a base station (BS)operable to communicate with a user equipment (UE), wherein the BSincludes at least one processor configured to: define a set ofcyclically permutable (CP) codewords, a plurality of cyclic shifts beingderivable from each CP codeword, each cyclic shift being distinct fromany other cyclic shift derivable from the set of CP codewords; select aCP codeword from the set; and encode the selected CP codeword into asynchronization signal to be sent to the UE, the encoding beingfacilitated by a repetitive cyclically permutable (RCP) codewordderivable from the selected CP codeword, a plurality of cyclic shiftsbeing derivable from the RCP codeword, each cyclic shift derivable fromthe RCP codeword being distinct from any other cyclic shift derivablefrom the RCP codeword, wherein the RCP codeword has a plurality ofcodeword elements each associated with a value, the value of at leastone codeword element in the RCP codeword being repeated in anothercodeword element position in the RCP codeword.
 28. The mobilecommunication system of claim 27, wherein the set of CP codewords isexpressed as:$\left( {c_{1},c_{2},{\ldots \; c_{i}\ldots},c_{\lceil\frac{M}{2}\rceil}} \right),{{where}\mspace{14mu} \left\lceil \frac{M}{2} \right\rceil}$is the smallest integer not less than M/2, 0≦c_(i)≦N, 1≦i≦M for all i,M, N are positive integers.
 29. The mobile communication system of claim28, wherein the RCP codeword is expressed as ({tilde over (c)}₁, {tildeover (c)}₂, . . . , {tilde over (c)}_(M)) with {tilde over(c)}_(2k-1)={tilde over (c)}_(2k)=c_(k), k=1, 2, . . . , M/2, where M isan even number.
 30. The mobile communication system of claim 28, whereinM=4, and the set of CP codewords is expressed as (c₁, c₂), the pluralityof cyclic shifts being derivable from each CP codeword is expressed as:(c₁, c₂) and (c₂, c₁).
 31. The mobile communication system of claim 29,wherein M=4, the RCP codeword is expressed as ({tilde over (c)}₁, {tildeover (c)}₂, . . . . , {tilde over (c)}_(M))=(c₁, c₁, c₂, c₂), and theplurality of cyclic shifts being derivable from the RCP codeword isexpressed as: (c₂, c₁, c₁, c₂), (c₂, c₂, c₁, c₁), (c₁, c₂, c₂, c₁) and(c₁, c₁, c₂, c₂).